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作者：Beffara, V
作者单位：Universite Paris Saclay
摘要：We prove that the Hausdorff dimension of the trace of SLE6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all kappa < 8, the SLEkappa trace has cut-points.
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作者：Dupuis, P; Nuzman, C; Whiting, P
作者单位：Brown University; AT&T
摘要：In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the distribution of various interesting quantities (such as the fraction of cells that contain a given number of balls), these expressions are often of limited practical use. Approximations provide an attractive alternative, and in the present paper we consider a l...
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作者：Gamboa, F; Lozada-Chang, LV
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universidad de la Habana
摘要：We consider the set M, of all n-truncated power moment sequences of probability measures on [0, 1]. We endow this set with the uniform probability. Picking randomly a point in M, we show that the upper canonical measure associated with this point satisfies a large deviation principle. Moderate deviation are also studied completing earlier results on asymptotic normality given by Chang, Kemperman and Studden [Ann. Probab. 21 (1993) 1295-1309]. Surprisingly, our large deviations results allow us...
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作者：Pène, F
作者单位：Universite de Bretagne Occidentale
摘要：The motivation of this work is the study of the error term e(t)(epsilon)(x,omega) in the averaging method for differential equations perturbed by a dynamical system. Results of convergence in distribution for ( e(t)(epsilon) (x,.)/ rootepsilon) epsilon>0 have been established in Khas'minskii [Theory Probab. Appl. 11 (1966) 211-228], Kifer [Ergodic Theory Dynamical Systems 15 (1995) 1143-1172] and Pene [ESAIM Probab. Statist. 6 (2002) 33-88]. We are interested here in the question of the rate o...
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作者：Ball, F; Neal, P
作者单位：University of Nottingham; Lancaster University
摘要：This paper is concerned with a stochastic model for the spread of an epidemic among a population of n individuals, labeled 1, 2,. .., n, in which a typical infected individual, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently according to the contact distribution V-i(n) = {nu(i, j,)(n) ; j = 1, 2,. . . n}, at the points of independent Poisson processes with rates gimel(G)(n) an...
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作者：Bass, RF; Chen, X
作者单位：University of Connecticut; University of Tennessee System; University of Tennessee Knoxville
摘要：If beta(t). is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee(gammabeta1) is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for beta(1) and -beta(1). We establish lim sup and lim inf laws of the iterated logarithm for beta(t) as t --> infinity.
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作者：Albeverio, S; Kondratiev, Y; Pasurek, T; Röckner, M
作者单位：University of Bonn; University of Bielefeld; University of Bielefeld
摘要：We present a new method to prove existence and uniform a priori estimates for Euclidean Gibbs measures corresponding to quantum anharmonic crystals. It is based first on the alternative characterization of Gibbs measures in terms of their logarithmic derivatives through integration by parts formulas, and second on the choice of appropriate Lyapunov functionals.
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作者：Bank, P; El Karoui, N
作者单位：Humboldt University of Berlin; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We study a new type of representation problem for optional processes with connections to singular control, optimal stopping and dynamic allocation problems. As an application, we show how to solve a variant of Skorohod's obstacle problem in the context of backward stochastic differential equations.
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作者：Hu, YY; Shi, Z
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine tools in stochastic calculus, including Kotani's lemma and Lamperti's representation for exponential functionals. In particular, our result for quenched moderate deviations is in agreement with a recent theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 571-609] who studied the corresponding proble...
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作者：Mendelson, S; Schechtman, G
作者单位：Australian National University; Weizmann Institute of Science
摘要：We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization techniques and tail estimates of norms, viewed as random variables on Euclidean spheres. The estimates of shattering dimensions can be applied to obtain error bounds for certain classes of functions, a fact which was the original motivation of this study. Althoug...
